Three dimensional simulation of fluid flow in X‐ray CT images of porous media

A numerical scheme is developed in order to simulate fluid flow in three dimensional (3‐D) microstructures. The governing equations for steady incompressible flow are solved using the semi‐implicit method for pressure‐linked equations (SIMPLE) finite difference scheme within a non‐staggered grid system that represents the 3‐D microstructure. This system allows solving the governing equations using only one computational cell. The numerical scheme is verified through simulating fluid flow in idealized 3‐D microstructures with known closed form solutions for permeability. The numerical factors affecting the solution in terms of convergence and accuracy are also discussed. These factors include the resolution of the analysed microstructure and the truncation criterion. Fluid flow in 2‐D X‐ray computed tomography (CT) images of real porous media microstructure is also simulated using this numerical model. These real microstructures include field cores of asphalt mixes, laboratory linear kneading compactor (LKC) specimens, and laboratory Superpave gyratory compactor (SGC) specimens. The numerical results for the permeability of the real microstructures are compared with the results from closed form solutions. Copyright © 2004 John Wiley & Sons, Ltd.     

Numerical manifold method for dynamic nonlinear analysis of saturated porous media

It is well known that the Babuska–Brezzi stability criterion or the Zienkiewicz–Taylor patch test precludes the use of the finite elements with the same low order of interpolation for displacement and pore pressure in the nearly incompressible and undrained cases, unless some stabilization techniques are introduced for dynamic analysis of saturated porous medium where coupling occurs between the displacement of solid skeleton and pore pressure. The numerical manifold method (NMM), where the interpolation of displacement and pressure can be determined independently in an element for the solution of u–p formulation, is derived based on triangular mesh for the requirement of high accurate calculations from practical applications in the dynamic analysis of saturated porous materials. The matrices of equilibrium equations for the second‐order displacement and the first‐order pressure manifold method are given in detail for program coding. By close comparison with widely used finite element method, the NMM presents good stability for the coupling problems, particularly in the nearly incompressible and undrained cases. Numerical examples are given to illustrate the validity and stability of the manifold element developed. Copyright © 2006 John Wiley & Sons, Ltd.     

About Darcy's law in non-Galilean frame

This paper is aimed towards investigating the filtration law of an incompressible viscous Newtonian fluid through a rigid non-inertial porous medium (e.g. a porous medium placed in a centrifuge basket). The filtration law is obtained by upscaling the flow equations at the pore scale. The upscaling technique is the homogenization method of multiple scale expansions which rigorously gives the macroscopic behaviour and the effective properties without any prerequisite on the form of the macroscopic equations. The derived filtration law is similar to Darcy's law, but the tensor of permeability presents the following remarkable properties: it depends upon the angular velocity of the porous matrix, it verifies Hall–Onsager's relationship and it is a non-symmetric tensor. We thus deduce that, under rotation, an isotropic porous medium leads to a non-isotropic effective permeability. In this paper, we present the results of numerical simulations of the flow through rotating porous media. This allows us to highlight the deviations of the flow due to Coriolis effects at both the microscopic scale (i.e. the pore scale), and the macroscopic scale (i.e. the sample scale). The above results confirm that for an isotropic medium, phenomenological laws already proposed in the literature fails at reproducing three-dimensional Coriolis effects in all types of pores geometry. We show that Coriolis effects may lead to significant variations of the permeability measured during centrifuge tests when the inverse Ekman number Ek⁻¹ is 𝒪(1). These variations are estimated to be less than 5% if Ek⁻¹<0.2, which is the case of classical geotechnical centrifuge tests. We finally conclude by showing that available experimental data from tests carried out in centrifuges are not sufficient to determining the effective tensor of permeability of rotating porous media. Copyright © 2004 John Wiley & Sons, Ltd.     

Upscaling of elastic properties for large scale geomechanical simulations

Large scale geomechanical simulations are being increasingly used to model the compaction of stress dependent reservoirs, predict the long term integrity of under‐ground radioactive waste disposals, and analyse the viability of hot‐dry rock geothermal sites. These large scale simulations require the definition of homogenous mechanical properties for each geomechanical cell whereas the rock properties are expected to vary at a smaller scale. Therefore, this paper proposes a new methodology that makes possible to define the equivalent mechanical properties of the geomechanical cells using the fine scale information given in the geological model. This methodology is implemented on a synthetic reservoir case and two upscaling procedures providing the effective elastic properties of the Hooke's law are tested. The first upscaling procedure is an analytical method for perfectly stratified rock mass, whereas the second procedure computes lower and upper bounds of the equivalent properties with no assumption on the small scale heterogeneity distribution. Both procedures are applied to one geomechanical cell extracted from the reservoir structure. The results show that the analytical and numerical upscaling procedures provide accurate estimations of the effective parameters. Furthermore, a large scale simulation using the homogenized properties of each geomechanical cell calculated with the analytical method demonstrates that the overall behaviour of the reservoir structure is well reproduced for two different loading cases. Copyright © 2004 John Wiley & Sons, Ltd.     

声波在水-多孔介质海底界面上的反射与透射

声波在海底界面的反射和透射是海底散射、海底混响、海底目标探测的重要问题。利用Biot多孔介质声传播理论对声波在水-多孔海底界面上的反射和透射进行了分析,具体给出反射声波的反射系数,3种透射声波的透射系数以及声能透射系数随入射波入射角和频率(10~40 kHz)的变化关系,分析了各种透射波对透射声能的贡献。多孔海底介质参数分别采用Stoll和Chotiros给出的2组参数进行理论计算。     

分层流体中内孤立波在潜浮式竖直薄板上透射和反射

采用边缘层理论研究了两层流体系统中内孤立波在潜浮式竖直薄板上的透射和反射问题,提出了非线性演化方程的“初值”条件,分析了内孤立波与薄板非线性相互作用的效应。研究表明:流体层的密度比以及薄板伸入上下层的深度对于反射和透射波结构具有显著的影响,薄板伸入下层越深、密度差越小,则薄板阻碍孤立波透射的效率越高;透射波通常演化为单峰孤立波和迅速衰减的尾波,反射波演化为缓慢衰减的尾波列;对于具有小密度差的跃层结构,内孤立波在潜浮式竖直薄板上的透射及其演化近乎是无障碍的。     

A Numerical Study on the Structure and Dynamics of Turbulence in Oscillatory Bottom Layer Flow over A Flat or Rippled Bed

1 .IntroductionUnder the influence of surface waves ,sandripples often appear on beaches . Whenthe amplitudeof water oscillationis sufficientlylarge ,vortices are formed onthe lee of every sand ripple crest . A-mongthese vortices ,the most important are t…     

分层海洋的内孤立波

本文从流体力学基本方程组出发,在非地转条件下导得了分层海洋的内孤立波方程—Kbv和mKdv方程,证实了在非地转条件下,一类海洋非线性波动是可以严格满足内孤立波方程的。在地转条件下采用f平面近似导出了KdV方程的演化形式一有源KdV方程,地转的影响含于源项中。由初步的分析得出,f对KdV方程的影响是微弱的。由已得的KdV和mKdV方程的解可知,内孤立波与线性波有着本质差别。     

波浪作用下海床动力反应的数值分析

近海和离岸建筑物的基通常处于连续不断的小风浪作用之下，可将其变形视为弹性。基于二维广义Biot理论，提出了线性或非线性波浪作用下饱和弹性海床动力应应的时域有限元数值解法。静力平衡条件和Biot方程组成的边值方程可视为其特例，在比较算例中，数值计算得到的孔压和有效应力幅值沿海床深度的分布与解析解十分吻合。土骨架和孔隙流体的加速度对海床动力反应的影响很小。具体算例表明，线性波沿缓坡海床传播时，土层中超静孔压和有效应力幅值随之增大，有可能发生滑动坡坏。所提出的数值解法能够灵活地处理非线性波浪荷载，海底复杂地质条件和波浪沿缓坡传播等复杂情况。